Elliptic curve isogeny class 17424.5-p over number field \(\Q(\sqrt{-2}) \)

• Base field: \(\Q(\sqrt{-2}) \)
• Label: 2.0.8.1-17424.5-p
• Conductor: 17424.5
• Rank: \( 1 \)

Base field \(\Q(\sqrt{-2}) \)

Generator \(a\), with minimal polynomial \( x^{2} + 2 \); class number \(1\).

Elliptic curves in class 17424.5-p over \(\Q(\sqrt{-2}) \)

Isogeny class 17424.5-p contains 6 curves linked by isogenies of degrees dividing 8.

Curve label	Weierstrass Coefficients
17424.5-p1	\( \bigl[a\) , \( 0\) , \( a\) , \( -47\) , \( -598\bigr] \)
17424.5-p2	\( \bigl[a\) , \( 0\) , \( a\) , \( -7\) , \( 2\bigr] \)
17424.5-p3	\( \bigl[a\) , \( 0\) , \( a\) , \( -620 a + 273\) , \( 2796 a - 9910\bigr] \)
17424.5-p4	\( \bigl[a\) , \( 0\) , \( a\) , \( 620 a + 273\) , \( -2796 a - 9910\bigr] \)
17424.5-p5	\( \bigl[a\) , \( 0\) , \( a\) , \( -87\) , \( -302\bigr] \)
17424.5-p6	\( \bigl[a\) , \( 0\) , \( a\) , \( -1407\) , \( -20102\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

\(\left(\begin{array}{rrrrrr} 1 & 4 & 2 & 2 & 2 & 4 \\ 4 & 1 & 8 & 8 & 2 & 4 \\ 2 & 8 & 1 & 4 & 4 & 8 \\ 2 & 8 & 4 & 1 & 4 & 8 \\ 2 & 2 & 4 & 4 & 1 & 2 \\ 4 & 4 & 8 & 8 & 2 & 1 \end{array}\right)\)

Isogeny graph